An Organizations and Incentives Critique of the Literature on Teacher Pay and School Governance

John Garen* Department of Economics

Gatton College of Business and Economics University of Kentucky

Lexington, KY 40506-0034 jgaren@uky.edu

October 2014

Abstact

This paper applies fundamentals of the economics of organizations and principal-agent theory to the ownership and governance of schools, the use of teacher incentive pay, and school reform efforts. We analyze schools as we do firms. Important element are the multitask principal-agent model and models of public/private differences in institutional incentives. Applying these models to schools, we find that many public school teachers will have attenuated incentives, but distorted towards test scores and that mandates to increase test score rewards may be counterproductive. Institutional reform seems more promising, where the goal is to alter school’s/schools administrators’ payoff to make them more responsive to educational value produced and less to political influences, thereby inducing more effective teacher incentive systems. We discuss and critique school reform efforts in this regard, including Tiebout competition, charter schools, voucher programs, and use of “best practice” and also appraise the empirical literature on evaluating these programs. We find that many reform efforts are lacking in addressing critical aspects of institutional incentives and that empirical studies often fail to distinguish between trivial and large changes in school incentive environments. JEL codes: J33, I28, L21

*For comments and consultation on previous versions, I thank William Hoyt, Lori Taylor, session participants at the Association of Private Enterprise Education conference and the Southern Economic Association meetings, and workshop participants at the University of Kentucky. I also thank the University of Kentucky’s Gatton College BB&T Program for support.

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I. Introduction

This article considers several fundamental facets of the literature on the

economics of organizations and principal-agent theory and brings them to bear on

critiquing and analyzing the literature on the governance of schools, the use and nature of

teacher incentive pay, the performance of schools, and school reform efforts. Essentially,

we analyze schools as we do firms. This approach, with a few exceptions, is absent from

the literature on teacher incentive systems and school reform. We argue that our

approach is essential in understanding and evaluating such issues.

The chronic underperformance of many public schools, despite the long-term

growth in resources devoted to public education, has generated a number of reforms. A

popular one is some form of teacher incentive pay that ties pay to student test scores.

Another is experimentation with allowing more parental choice, such as charter schools

and vouchers. Thus, our discussion focuses on teacher incentive pay and the governance

of schools, where the latter includes school ownership, decision rights, and competition.

We analyze and critique schooling policy using the same framework as when we analyze

policy for other firms and industries.

Though the relevant literature on organizations and incentives is geared toward

private, competitive organizations, it considers conditions that are quite relevant to

schools and provides important insights into teacher pay and school governance. Thus,

we develop a model of teacher incentive pay and school behavior in public versus private

schools, in competitive and non-competitive settings, and use it to consider the effects of

reform and to and critique aspects of the empirical literature on teachers and schools.

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Our critique and discussion focuses on the incentives imbedded in institutional/

organizational frameworks and how this affects pay setting for employees/teachers. It is

this perspective that is lacking in the education literature. We identify four parameters

that are key in determining the behavior of the organization/school and show how they

affect pay setting and organization performance. They are: (i) the degree of residual

income claimancy of the organization and/or concentration of interests of stakeholders;

(ii) how closely the organization’s revenue/budget is tied to value produced; (iii) the

importance of public/political symbols of success, and; (iv) the political strength of

employees/unions.

Each of these affects an organization in predictable ways, and perhaps in ways

that frustrate the goals of education policy. We argue that the appropriate way to address

education policy – following the economics of organization approach – is to understand

the role of these parameters and how they might be changed.

Our approach is based on a number of fundamentals in the literature. One is the

multitask principal-agent model of Holmstrom and Milgrom (1991) where incentives are

established for agents who do many tasks. Too great an incentive for one task leads to a

distortion of effort and a possible reduction in value. This issue is well recognized

regarding education and underlies the problem with mandates for rewarding test scores.

It is examined carefully in what follows.

A second fundamental idea is based on the work of Jensen and Meckling (1992),

who extend Hayek (1945). Jensen and Meckling (1992) stress the importance of

combining decision-making power with incentives to make good decisions and argue that

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decentralizing both decision making and incentives is especially critical where “specific”

knowledge – akin to Hayek’s knowledge of particular circumstances – is important.

In the context at hand, “specific knowledge” is knowledge of unique and subtle

characteristics of teachers, students, and schools. Much of this knowledge is held by

school administrators, teachers, and parents and is hard to quantify and transfer to others.

This is in contrast to general knowledge, such as standardized test scores, which is

straightforward to quantify and transmit. Governance and incentives for use of these

types of knowledge in the context of schools is detailed below.

Another fundamental from the literature is related to the work of Dixit (1997,

2002) and Acemoglu, Kremer, and Tian (2007), who contrast public and private

organizations in their provision of incentives to employees. Essentially, the payoff

function for public sector managers serves to attenuate managerial incentives and this

attenuation is passed along to employees. Naturally, since most schools are public

organizations, this analysis is quite germane.

We arrive at a number of broad conclusions from our approach:

(i) The applicability of our standard models is clear. These models consider

implementing a reward system in scenarios that schools face, i.e., where information on

employee performance is subtle, subjectively measured, and hard to assess.

(ii) School administrators have situation-specific knowledge about teacher

productivity that looms large. Using this knowledge is important but requires subjective

and discretionary evaluations and pay setting by school administrators.

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(iii) For use of subjective performance evaluations, the incentives for school

administrators to establish effective compensation policies for teachers matters. This

incentive depends on institutional/organizational features.

(iv) Public schools with little competition are likely to have weak incentives, with

any remaining incentives skewed toward test scores due to political factors. These

institutional incentives are “passed along” to teachers, diluting and distorting their

incentives.

(v) As is well-recognized, mandated test scores rewards for teachers distort their

effort away from other useful educational efforts. The institutional setting of the school

determines whether this harms or helps. If is harmful for schools in settings that

approximate a competitive market, though it may be helpful otherwise, but only if tests

are well designed. Also, this distortion appears even more unfavorable with the increased

realization by researchers of the importance non-cognitive skills.

(vi) Rather the use of mandates, our approach suggests a better framework for

reform is to alter the underlying institutional incentives, e.g., how budgets are tied to

value created, the extent of stakeholder incentives, and the degree of political influence.

(vii) There is a large body of empirical evaluations of this type of reform, e.g., of

charter schools and other choice programs. Most are not informative tests of the effect of

institutional reform because they compare widely divergent reform programs, or very

weak reforms, to regular public schools. For example, charter programs vary widely

regarding their availability, in their curricula and hiring autonomy, and none have the

ability to set their price. Some are almost indistinguishable from regular schools and

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others are markedly different. Thus, comparing a wide sample of charter schools to

regular schools may reveal little about the effect of institutional reform.

(viii) Other reforms efforts focus on the adoption of better practices and better test

score evaluation methods. Our approach indicates that this is problematic absent changes

in institutional incentives. Moreover, good institutional incentive are expected to

generate better practices without their mandate from above.

The outline of the remainder of the paper is as follows. Section II presents

important background literature, supporting the validity of our approach. Section III

begins the formal modeling by applying the Holmstrom-Milgrom model to teachers.

Section IV considers the standard model of pay setting by the competitive, private-sector

organization and applies this model to schools. Section V modifies the model to consider

the case of a school administrator/manager operating in a public organization facing little

competition. Here, the administrator’s payoff function is altered, causing teachers

incentives to be dulled and skewed.

Section VI considers the effect of mandating teacher incentives for test scores and

illuminates pitfalls of doing so. Section VII turns to institutional reform efforts and

empirical evaluations of such reforms in the literature. Section VIII considers adoption

of best practices from successful schools. Lastly, section IX concludes.

II. Some Background Literature

Though teacher characteristics such as certification and advanced degrees do not

have much effect on student test scores, recent empirical research shows that teachers do

make a difference. Rockoff (2004) and Rivkin, Hanushek, and Kain (2005), for example,

demonstrate that some teachers consistently have classrooms of students that outperform

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others on test scores and that this difference is quite sizable. More recent support for this

is in Chetty, et.al. (2014a,b).

There is ample evidence that teachers respond to incentives. As examples, Figlio

and Kenny (2007), Eberts, Hollenbeck, and Stone (2002), Lavy (2009), and Jacob (2005)

find that teachers respond largely as expected, i.e., the incentivized behavior increased.1

Jacob’s findings also suggest that teachers engage in “teaching to the test” rather than

broader educational efforts. This raises the issue that incentives for test scores will

distort teacher effort away from other educational activities.

Regarding the value of schooling, there is evidence that parents value better test

scores, but they also value other aspects of their children’s educational experience. See,

for example, Jacob and Lefgren (2007). Also, Heckman, Stixrud, and Urzua (2006) show

the importance of non-cognitive skills, which are not directly reflected in test scores.

Teachers presumably can be rewarded for nurturing such non-test score aspects of

education. There is considerable anecdotal evidence that school principals are well

informed regarding the quality and performance of their teachers in this regard. Jacob

and Lefgren (2008) provide formal evidence. This is not surprising since school

administrators work around their teachers every day, gaining information that is not

reflected in test scores. With the authority to do so, school administrators could use this

information to reward teachers. This more subjective measure of performance is likely to

capture a broader picture of the teacher’s contributions to educational value.

This brings up the issue of how situation-specific knowledge is utilized. Jensen

and Meckling (1992), following the ideas of Hayek (1945), argue that those who have the

1 Neal (2011) provides a more thorough review. Note that not all studies find an effect of teacher incentives. See, for example, Fryer (2013).

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knowledge ought to have the incentives to use it appropriately. This speaks to the

ownership and governance of schools and is modeled in what follows.

The difficulties of implementing a reward system based on complicated, subtle,

subjectively measured, and hard to assess aspects of jobs have been pointed out and

analyzed in detail in the private-sector, competitive setting. See Prendergast (1999) for a

survey. It is well recognized (e.g., Lavy (2007)) that these issues apply in education.

Neal (2009) points out that, despite these difficulties, the competitive process encourages

the most efficient incentive systems and human resource practices. This competitive

process is often lacking for public schools and is discussed extensively below.

A significant literature examines differences between public- and private-sector

enterprises. Naturally, this is particular important for schools since most are in the public

sector. The papers of Dixit (1997, 2002) and Acemoglu, Kremer, and Tian (2007) are

especially relevant since they discuss how the public sector organization alters incentives

of employees. In their models, political constraints alter the payoff function for public

sector managers. They find that their incentives are dulled, which is passed along to

public organization employees. Below, we build these ideas into our model.

Note that school competition and school choice alters the organization’s

incentives by enabling parents to more easily move their children and funding from

schools. Podgursky and Ballou (2001) argue that this can induce school administrators to

adopt efficient reward systems for teachers. Hanushek and Rivkin (2004) and Neal

(2009) make similar arguments. We model this below.

Various parts of the literature make the case for taking the approach of this paper.

It is clear that teachers matter in producing educational value and that incentives affect

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teacher behavior. Cognitive and non-cognitive skills are important. School

administrators have knowledge about teachers that could be used to provide incentives.

The effects of consumer choice and competition are mainstays in economics analysis and

the analysis of public-private sector differences is well established. It seems quite

sensible to apply these models to schools, i.e., to model schools as we do firms.

III. Teacher Assessment, Test Scores, and Incentives for Teachers

A. Applying the Principal-Agent Model to Teachers

Many issues regarding incentive pay for teachers can be illustrated with a

standard multitask principal-agent model derived from Holmstrom and Milgrom (1991).

This model has been used widely to understand compensation arrangements in the private

sector in situations not unlike those of school teachers. i.e., where some aspects of jobs

are easy to quantify and others quite difficult.

Consider three broad aspects of teacher performance and effort that can affect the

educational value produced: T = the test scores of the teacher’s students; A = the school

administrator’s assessment of the teacher’s performance; and N = aspects of teacher

performance that are not observed by third parties. Define educational value as V and let

V be increasing in T, A, and N as V=V(T,A,N). Only the first two types of effort are

measured (with error) and so compensation can be based on these two. The first of the

two can be objectively measured and while the second cannot.

Note that A reflects specific knowledge, i.e., knowledge acquired by the school

administrator that is specific to the school and teacher that is difficult to summarize and

transmit elsewhere. One must rely on the school administrator to use this knowledge and

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is like subjective performance evaluation in standard principal-agent models. In contrast,

T is information that is readily summarized, transmitted and understood by others.

The nature of the test underlying T determines the value of good scores to

education as well as the nature of teacher effort in this regard. For a narrowly designed

test, this may entail narrow effort, e.g., a focus on computational math problems. Also, if

the test is easily “gamed,” it also may involve “strategic” effort such as teaching specific

problems or taking steps so that low-achieving students do not take the exams. For these

cases, tests, the marginal product of T in producing educational value, VT, is very small.

The administrator’s evaluation, A, is expected to reflect broader, less objectively-

defined aspects of teacher effort, e.g., effort directed at communication, problem solving,

creativity as well as effort in teamwork and in dealing with parents. This also includes

nurturing intangible, non-cognitive skills such as hard work, perseverance, and

responsibility. The unobserved aspect of teacher performance, N, is likely to reflect

similar efforts regarding intangibles and less objectively-measured outcomes.

Following the standard model, assume that teachers are risk averse with a

constant absolute risk aversion utility function. The teacher’s certainty equivalent of

utility is given by U = E(Y) – C(T,A,N) – ½ρR, where E(Y) is the teacher’s expected

income, C(∙) is the utility cost of effort, ρ is the coefficient of absolute risk aversion, and

R is the variance of teacher income due to error in measuring true efforts. The school

administrator observes T and A (with error) and sets compensation as a linear function2

of T and A such that E(Y) = b0 + bTT + bAA.

2 Actual rewards for teachers are likely to be nonlinear; indeed Ahn (2008) and Vigdor (2008) find this is the case for North Carolina’s rewards to teachers for better test scores. Linearity is a simple and tractable way to capture the idea that rewards are tied to T and A.

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Teachers select the three types of effort, T, A, and N, to maximize utility given by

U = E(Y) - C(T,A,N) - ½ρR = b0 + bTT + bAA - C(T,A,N) – ½ρR. This entails choosing

each type of effort to equate its marginal benefit its marginal effort cost. This is a

standard model with straightforward results. Effort on T rises with bT and effort

regarding A increases with bA, i.e., ∂T/∂bT > 0 and ∂A/∂bA > 0. The cross-effects of bT on

A and of bA on T, as well as how N is affected by incentives are also important. In

formal terms, these depend on the cross-partial derivatives in the cost of effort function.

The intuitive interpretation of this is quite sensible.

Consider the “virtuous” case where each type of effort facilitates the other, that is,

each lowers the marginal cost of the other; CAT, CNT, and CNA are all negative. Here, an

increase in either incentive raises all types of effort. The more plausible (and worrisome)

case is where more effort in improving the test results impedes effort on A and N, i.e., T

raises the marginal cost of A and N, implying that CTA>0 and CTN >0. Also, given the

way A and N are defined, more effort on one aids that of the other, implying that CAN<0.

These entail that a greater reward for the test, bT, reduces other aspects of teacher

effort: ∂A/∂bT < 0 and ∂N/∂bT < 0. Thus, stronger incentives for test scores thus do not

unambiguously increase educational value. Also, greater reward for the administratively

measured effort, bA, increases the unobserved aspects of output but reduces test scores:

∂N/∂bA > 0 and ∂T/∂bA < 0.

These simple results underlie much of the debate regarding the use of test scores

as incentives for teachers: that it diverts teachers from other important educational tasks,

perhaps to the detriment of educational value. This is especially likely for poorly

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designed and/or easily gamed tests. For these types of tests, test scores do not correlate

well with educational value, implying a low value for the marginal product of T, VT.

Also, for low-quality tests, teacher effort to raise test scores tends to be narrow and non-

complementary to other educational efforts. Thus, encouraging better scores on poorly

designed tests serves to add little to education directly and reduces value by distorting

behavior away from other value-raising effort.

B. What Does the Literature Say . . . And Not Say?

The difficulties of measuring the contribution of teachers and the potential

shortcomings noted above of rewarding student test scores are well recognized. Neal’s

(2011) review is an example. An extensive compilation this research – in economics,

education, and psychology – is in the National Research Council study of Hout and Elliot

(2011) while Neal’s (2011) review focuses on the work in economics. Generally

speaking, the literature finds that incentives do affect behavior as one might expect.

However, one of Hout and Elliot’s (2011) conclusions is that “incentives will often lead

people to find ways to increase measured performance that do not also improve the

desired outcomes.” As result, they recommend a cautious design and implementation of

incentive plans, with further research and evaluation.

Similar concerns have been raised about a currently popular approach to

evaluating teachers for possible use in incentive plans using so-called teacher value

added. This approach examines the effect of individual teachers on the before and after

test scores of students. Chetty, Friedman, and Rockoff (2014a,b) examine this method

and the controversies associated with it at great length. Concerns have been raised

regarding whether value added actually captures teacher performance and whether this

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measure corresponds to true value or just “teaching to the test.” If the latter holds, greater

rewards for value added are mostly misdirected incentives.

Though Chetty, et. al. (2014a,b) find that value added is a robust measure of

educational value, there is a deeper difficulty to be addressed. Commentators

recommend that good performance measures be developed and used appropriately in

incentivizing teachers. But how, or by what process, might this be accomplished? More

specifically, who implements the reward system and what are their incentives? Might

we expect them to behave as commentators wish? Policy makers presumably ought to

know these answers in devising recommendations since they will affect policy outcomes.

This is where the economics of organizations plays an important role in understanding

institutions and their incentives.

Regarding the standard incentive pay model for the private sector, a profit

maximizing firm in a competitive environment chooses the parameters of the

compensation plan for its agents. In these models, similar issues arise here as with

incentives for teachers: workers may have jobs with tasks that are difficult to measure;

available measures may be quite imperfect; rewards for one measure can distort effort in

undesirable ways; there is subjective and specific knowledge on worker efforts that is

often available. This literature recognizes that each of these presents difficulties and

trade-offs, but ultimately it is the incentives implicit in competitive markets that

determine pay setting.3

The environment in most schooling markets is usually quite different; schools

operate with a mix of political and economic constraints. Thus, it is worthwhile to

characterize the institutional setting/incentives in this environment for those who 3 See Prendergast (1999) for a survey.

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determine compensation practices. We turn to this in the next two sections and use the

findings for further critique of the literature.

IV. The Competitive Model of Incentive Pay

We initially consider pay setting by schools as we would for the competitive firm.

As in the incentive pay literature, this model is viewed as predicting how firms/schools

behave in this economic setting, as well as establishing a benchmark for comparison.

As in the standard, competitive model, consider the school administrator’s payoff

function as being closely approximated by the net income of the school. This can result

from the administrator being the owner of the school or an employee-manager of a

private organization with the appropriate incentives.4 Assume that the school operates in

a competitive market and sells schooling services for their value, V, and also competes

for teachers.5

Thus, the payoff function per teacher for the school administrator is F = E(V – Y)

= V(T,A,N) – (b0 + bTT + bAA).6 The payoff maximizing compensation schedule is

chosen subject to the incentive compatibility and individual rationality constraints from

principal – agent theory. With these constraints, the payoff function becomes F =

V(T,A,N) – C(T,A,N) - ½ρR - UM, where UM is teacher alternative utility.

The outcome of this model most instructive with further simplifying assumptions:

assume that the V function is linear; V = αTT + αAA + αNN, and assume risk neutrality for

4 With administrators as the hired managers of school owners, the principal-agent problem emerges regarding how to provide incentives for school administrators. Thus, one might consider another layer of incentives with owners providing incentives to the administrators who then set incentives for teachers. Rather than trying to model more steps in this hierarchy, we focus on just two. Note that this issues arises in the standard model where firm owners wish to provide incentives to firm managers. 5 It is important that school-firms are free to set prices so revenue reflects value, V. Failure of this generates some issues to be discussed below. 6 We assume constant returns to scale in the number of teachers so the maximum payoff is attained by maximizing net value per teacher. Capital costs are assumed to be fixed and therefore suppressed.

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all parties. These enable simple solutions without taking away from the basic, underlying

economic implications. This model implies that firms/schools set incentives as:

(1) bT = αT - αNCNT/Ω

(2) bA = αA - αNCNA/Ω

where Ω >0 based on second-order conditions.

Since the marginal product of T is αT and that of A is αA, one can see how rewards

for each type of effort diverge from the marginal products of the observed efforts. When

CNT>0 (the plausible case), bT is less than αT. This is because bT distorts effort away

from N, so generates a lower incentive for T. Also, because increasing effort regarding A

lowers the marginal cost of N (CNA<0), then bA> αA. More effort for A also increases N,

inducing a higher bA.

Note that it is the environment of profit maximization in competitive markets that

induces organizations to set their compensation systems in this manner. In this setting,

the desirability of rewarding tests scores depends the quality of the test. Low-quality

tests have a low αT (a low marginal product) and impede efforts regarding N, implying a

high value of CNT. These induce the firm to set a low bT. When the complementarity of

A and N is large (a high CNA), then firms set stronger rewards for the subjective,

administrative evaluation. These foreshadow the potential pitfalls of mandating heavy

reliance on rewarding T.7 Of course, most educational organizations do not operate in a

competitive, private-sector environment. We turn to this issue next.

V. Pay Setting in Noncompetitive, Public Organizations

7 In the more general case with risk aversion of teachers, these basic results arise, though with some adjustment. Risk aversion tends to reduce bT and bA, assuming that T and A are measured with error, since they introduce risk into the teacher’s compensation.

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This section considers how pay for agents is established in the public and/or

noncompetitive sector. The results are used to inform our critique of studies of teacher

incentives and school organization.

A. Public Sector, Noncompetitive Organizations

There is a substantial literature regarding the behavior of organizations in the

public and/or noncompetitive sector. We apply its findings and related ideas to pay

setting by school administrators. Most schools are public sector enterprises. Differences

from the private, competitive setting emerge because the different institutional setting

alters the payoff function of managers/school administrators which, in turn, alters how

they establish pay and incentives for teachers. Autonomy over pay setting for such

organization translates into a different – and problematic – incentive system for teachers.

A number of distinctions are drawn between private and public institutions. Some

key ones are the following. Public institutions rely on taxation for their funds rather than

voluntary sources. Output is not directly sold to users. These put less pressure on public

agencies to provide value and cover costs. This is related to the idea that voters are often

rationally ignorant and so public sector outcomes are overly influenced by special

interests. Also, public institutions are not structured so that managers (or anyone) are

residual income claimants. These imply that the payoff functions of public sector

officials need not be well aligned with net value.

Several theoretical papers in the literature provide formal models based on related

ideas. Dixit (1997, 2002), building on the multitask principal-agent model of Holmstrom

and Milgrom (1991) and the common agency work of Bernheim and Whinston (1986),

develops a model where the government agent has multiple principals. The principals are

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akin to a politician’s constituents, each with different objectives that pull the government

agent in many directions. This ends up diluting the government agent’s payoff for

pursuing any single objective.

Acemoglu, Kremer, and Mian (2007) develop a model in the context of rewards

for student test scores with similar implications. In their model, politicians are

responsible for many public agencies, including schools. They are rewarded by voters

based on school performance as well as a host of other policies unrelated to schools.

Thus, the politician may lose office for reasons unrelated to school performance. This

implies that the politician’s payoff function with respect to the school system is (1- π)

times the value added of the schools, where π is the probability of losing one’s office for

reasons extraneous to schools. This payoff function dilutes the politician’s incentives to

pursue value maximizing schools.

The above models imply that the payoff to public sector managers depends on net

value creation, but in a weak or diluted way, e.g., FP = θ(V-Y), where FP is the manager’s

payoff function and θ<1. The dispersion of incentives and knowledge of stakeholders in

the organization (voters versus shareholders) for the public sector generate this results.

We start with this payoff function but consider refinements based on related features of

public institutions and public schools.

First, note that the revenue of a public school is its budget and is determined by a

political process. This process is such that changes in value produced by the school are

not necessarily well reflected in school revenue. Letting B represent the school’s budget,

this is expressed as B=B(V), with 0<B’<1. It is unlikely that B’=0, i.e., that there is no

link between V and B, since bad enough outcomes will cause repercussions for the

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school’s budget. Still, we expect B’<1, implying that the political process mutes the

relation of V to B.

For schools in a non-competitive environment, a related outcome is likely. In a

competitive setting, total revenue received for delivering value V equals V. If value falls

(rises) by $1, total revenue falls (rises) by $1. Where there is less competition, the

revenue received may not fall dollar-for-dollar with changes in value. For schools that

deliver a lower V, parents have few options and many will continue to send their children

to the school and the school’s total revenue does not fall commensurately. This

reinforces the outcome of the previous paragraph that the relationship between the

school’s revenue and changes in V is attenuated.

Another important aspect of the public sector is that there is no lawful residual

income claimancy, i.e., school administrators cannot keep net school revenue, B(V) – Y.

Thus, the utility gained by the administrator from an operating surplus is not the value of

the surplus itself. It is unlikely to be zero, however, since the administrator’s job

probably is safer when the budgeted revenue covers cost. Also, the residual of revenue

over cost might be spent on workplace amenities. Still, the benefits are less than if

provided in cash. This reinforces the idea that the public administrator’s payoff depends

on net revenue school in a muted way so that FP = θ(B-Y), where θ<1.

A third aspect of the public sector is the importance of visible actions in

influencing voters since it is the political support of voters that weigh heavily in

determining the school’s budget and not simply the satisfaction of the parents of children

at the school. Visible, positively perceived actions enhance political support.

Administrators who engage in such actions will improve their payoff. Test scores are

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easy to report and are widely visible to the populace and so good scores are especially

helpful in generating political support. This is less true of aspects teacher performance

measured by the administrator, A. This involves subtle judgments that are difficult to

convey to the public. Thus, higher test scores will be weighted move heavily in the

administrator’s payoff function. Assume that test scores carry the weight δ>1.

Putting all of the above together yields a public sector administrator payoff

function of FP = θ(B(V)-Y), where T in the V function carries a greater weigh δ.

Combining this with the individual rationality constraint and risk neutrality, this becomes

FP = θ(B(V) - C). Assuming V being linear as V = αTT + αAA + αNN, this gives FP as

FP = θ(B(δα TT + αAA + αNN ) - C).

A related possibility is that administrators benefit by making teachers happier,

especially if a teachers’ union has a strong political voice. This suggests that teacher

utility, given by Y – C, enters into the school administrator’s payoff function. However,

raising teacher utility by handing cash over to teachers is a highly visible action that will

create negative publicity and reduce political support. So suppose that teacher pay, Y, is

politically fixed at Λ. With administrator payoffs depending on teacher utility, this gives

FP = θ(B(V) - Λ) + φ(Λ - C) = θB(V) – φC + (φ – θ)Λ, where φ>1 is the weight put on

teacher utility. With Λ fixed, the administrator acts to maximize θB(V) – φC. This is

identical to the above payoff function with φ>1 replacing θ<1 as the weight on C.

B. Pay Setting

The school administrator chooses compensation policy to maximize FP. For ease

of solution and exposition, let the budget function B(V)=B∙V = B∙(δαTT+αAA+αNN),

where 0<B<1. Then the solution is a simple transformation of those (1) and (2) and is:

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(3) bT = (θB/φ)[δαT - αNCNT/Ω]

(4) bA = (θB/φ)[αA - αNCNA/Ω]

where φ>1 or φ= θ depending on the form of the administrator’s payoff function.

Because B<1 there is a tendency for incentives to be reduced. This is reinforced

when φ> 1 and θ < 1. Recall that θ<1 and B<1 reflects the muted benefits to the

administrator of raising value. This attenuation of incentives for administrators is

“passed along” to teachers. Having φ>1 further supports this result. Essentially, because

administrators have weak incentives, so do teachers.

The exception to this is test scores. Because of their visibility and potential for

political support, the benefit of providing incentives for T is magnified by the factor δ>1.

Thus, incentives for T may be stronger than for the competitive, private case, depending

on the net effect of their increased visibility versus the above-discussed diluting effects.

However, relative incentives are altered. The ratio of the test score incentive to the

measured performance incentive is bT/bA. It is larger here than in the competitive, private

case because the factor δ magnifies test score rewards for the public sector.

Figure 1 illustrates this outcome. Point G is the equilibrium in the competitive,

private schools case. It is at the tangency of school isovalue curve V1, teacher

indifference curve C1, and a line of slope bT/bA. reflecting the relative price of T and A.

In the noncompetitive, public sector case the equilibrium is given at point J. Here, there is

a tangency of bT/bA to teacher indifference curve C0 and to the isovalue curve distorted

by the public, noncompetitive payoff function, θB(V0). As illustrated, point J shows

reduced and skewed incentives.

20

Figure 1

It is this characterization of public school teacher incentives and incentive-setting

that we use below in our critique of the literature. The institutional setting of the school

is determined by the parameters B, θ, δ, and φ and their effects should be accounted for

when examining the efficacy of proposed policies.

C. The Nonprofit Organization

Before proceeding, note that the private, nonprofit organization is common for

schools, e.g., those with religious affiliation. They have residual income claimancy, but

their legal, nonprofit status limits the distribution of the residual. Many charter schools

A bT/bA

C1

V1 C0

T

G

V0 J

bT/bA

O

θB(V)0

21

also are nonprofits. Their budget is determined by student enrollment, not by a political

process, so their net income is B-Y, though the revenue per student is usually mandated.

That nonprofit organizations cannot take their residual income in cash suggests

similarities to the public sector. However, many factors weigh against this. Nonprofits

are supported by stakeholders interested in promoting the value of educational services

provided, V. School administrators who raise V are more likely to succeed in their jobs.

Thus, the gains from a higher V is heightened in a nonprofit organization relative to the

public one. The private, nonprofit firm in a competitive setting seems more much more

like competitive, private, profit-seeking firm than a public organization.

VI. Mandating Rewards for Test Scores: Institutions Matter

If point J in Figure 1 is a good approximation of many public schools, one sees

the issue with teacher pay. Given their institutional environment, public school

administrators dull teacher incentives to the detriment of school performance. Perhaps a

natural reaction is to mandate teacher incentives. Doing so from the outside must rely on

generally available information, which implies reliance on test scores. Many states have

implemented teacher rewards based on the test scores at each school and there is

increasing interest in measuring and rewarding individual teacher performance in this

way. With the increased emphasis on rewarding test scores comes an implicit reduction

in the ability of school administrators to reward teachers based on their evaluations of

teacher performance. In effect, discretion is removed from the school administrator in

setting pay. Here we account for the institutional setting when considering how this is

likely to affect schools and the value of educational services provided.

22

In this analysis, consider two sorts of distinctions. One is between good and bad

tests. This depends on the two features discussed above: the marginal product of test

scores and the non-complementarity of effort on test scores to A and N. The other

distinction is between “good” and” bad” schools. Good schools are those that reasonably

approximate the outcome of point G in Figure 1.8 Bad schools are those that approximate

point J. The former occur in environments where the parameters B, θ, δ, and φ are all

close to one and the latter are the converse.

Now consider the effects of mandating rewards for different types of tests and

schools. A mandated value of bT above what the school would otherwise set requires an

increase in bT/bA. For good schools that approximate the equilibrium at point G, any

mandate of bT/bA is distorting and reduces net welfare. This reduction is worse if the test

is bad, but has negative consequences even if the test is good.

The more relevant case is that of bad schools at point J that have dulled and

skewed teacher incentives. The question is whether a mandate to increase the reward for

test scores improves outcomes or not. This depends on whether the test is bad or good.

When a mandate for higher test score rewards is put in place, teachers shift effort

toward generating higher test scores and away from other types of effort, causing T to

rise. For bad tests, this adds little (if any) to educational value while distorting effort

away from A and N. Since the latter reduces value, the net effect is to lower educational

value. For good tests, this is less likely to be the outcome. Increasing T raises value and

good tests have smaller non-complementarities to A and N, so they are not distorted as

much. An increase in value produced is much more probable.

8Perhaps induced by strong Tiebout competition. This is discussed below.

23

Thus, accounting for the institution setting of schools, i.e., the parameters B, θ, δ,

and φ, provides a more nuanced critique of mandating higher rewards for tests scores.

While it is true that such mandates distort teacher incentives, this policy for an entire state

will have negative consequences for the good schools in the state but positive

consequences for the set of bad schools. However, the latter holds only if the test is well

designed. If not, the unwanted outcome from the bad institutional setting is made worse.

Questions about the validity of tests mandated by state departments of education have

often been raised. If these concerns are legitimate, mandates for increased test score

rewards have negative consequences.

VII. Reform, Evaluating Reform, and Institutions

Recall that the objective function for the public school administrator is:

(5) FP = θB(δα TT + αAA + αNN) – φC,

where φ may equal θ. Our analysis implies that the four parameters B, θ, δ, and φ

characterize the institutional setting of the school and determines the school’s pay setting

and performance. These parameters represent the following:

θ = the degree of incentives and knowledge of stakeholders (shareholders or voters) of the organization and/or residual income claimancy, with θ ≤ 1; B = how closely tied the organization’s revenue is to value produced, B ≤ 1;

δ = the importance of public/political symbols of organization success, δ ≥ 1;

φ = the political strength of employees of the organization; φ ≥ 1.

Any analysis of policy towards schools should take account of these parameters for the

organizations involved.9 Do the values of the parameters indicate that school

administrator incentives are to vigorously pursue policies given from above? Do the

9 Coulson (1999) discusses a similar set of items that affect school incentives.

24

policies themselves fundamentally change these parameters for the institution that would

lead it to desired outcomes? If not, then it seems that the fundamental incentives of the

organization has not been altered and reform efforts are likely to be ineffectual. We take

this perspective in critiquing many of the studies and approaches to examining school

reform policies.

A. School Choice via Mobility: Tiebout Competition

School choice is a way of altering school governance and the administrator’s

payoff function. One avenue it does so is by raising the responsiveness of the school’s

revenue (or budget) to V. i.e., it raises the parameter B. It does so by allowing parents to

move their child and the funding if the parents believe value is not being delivered.

Tiebout competition may occur where there are multiple schools and/or school

districts and people choose among schools by choosing their residence in the appropriate

catchment area. Schools delivering a low V will have outmigration, presumably resulting

in a lower budget. There is considerable discussion in the literature whether Tiebout

competition can serve as a competitive force to discipline public schools. Probably the

best known study in this regard is Hoxby (2000), who finds that this form of competition

improves school test scores. Rothstein (2007) disputes this result, however. In related

study, Hoxby (2002) finds that Tiebout competition changes teacher hiring practices

toward more emphasis on teacher science and math skills, stronger college preparation,

and teacher independence and effort.

However, one might ask how effective Tiebout competition can be in increasing

the parameter B. This type of competition requires changing residence to change

schools, which can be quite costly, and so can be a very cumbersome form of choice.

25

Choice of residence involves consideration of a host of factors in addition to schools, so

catchment areas may lose or gain residents due to other factors. This lessens the

competitive effect on schools. Moreover, school districts may respond to mobility by

keeping the existing schools intact and redrawing catchment areas to maintain enrollment

in all schools. Thus, regardless of how bad the school is, it may be guaranteed attaining

full enrollment and retaining its funding. No school administrator will see declining

enrollment and suffer its negative consequences.

This suggests that school reform efforts that rely largely on Tiebout competition

may or may not change school administrator incentives much, depending on the mobility

of families in the relevant locations and on the (in)ability of school systems of offset

enrollment changes due to this mobility. Thus, its effects on school performance depends

on these two factors. The empirical work in the literature has not addressed this.

Regardless of any shortcomings of this form of competition, its importance has

likely declined considerably during the 20th century in the U.S. Hoxby’s (2004) overview

shows that, within this time period, the number of school districts in the U.S. fell from

over 100,000 to less than 20,000 and the share of local funding for public schools fell

from over 80% to less than 45%. Both suggest a diminished role of Tiebout competition.

B. “Zero-Sum” Choice Programs: Magnets and Open Enrollment

Other institutional reform efforts that entail a degree of school choice – and

presumably increase the parameter B – are magnet schools and open enrollment

programs. Magnet schools typically target an educational specialty and enroll a limited

number of students; often the top students in that specialty. The remaining students are

allocated to the other schools. Open enrollment programs allow students to enroll in

26

many schools in the district. Usually, the best schools fill up quickly and other schools

are allotted the remaining students. These programs seem to have the potential for

rewarding good schools (and raising B). But because remaining students are allocated

elsewhere, even bad school are virtually guaranteed full enrollment and retention of

funding. This indicates that B remains low. This is the “zero-sum” nature of these

programs; individual schools, and the school system, has net zero change in enrollments.

No school administrators have to suffer ill-consequences of declining enrollment and a

declining budget. Any remaining incentive is the likely preference for having the better

students at the school rather than the worst. Therefore, these are expected to do only a

little to raise the value of B.

The above illustrates how the open entry and exit conditions in a competitive

market, where new firms may enter and supplant inefficient ones, can sharpen incentives.

It establishes a stronger link between value created and the firm’s revenue. This is

missing from most open enrollment and magnet programs since the number of school-

firms is fixed and established by a central authority. Nobody goes “out of business.”

C. Vouchers and Charter Schools

These the two types of institutional reform seem to offer more extensive choice

and have the potential for substantial change in the parameter B, and well moving the

other parameters – θ, δ, and φ – closer to one. A number of issues arise in this regard

and are addressed below.

(i) Entry and Exit

Vouchers and charter schools have more potential in avoiding the entry and exit

problem noted above. This is particularly true if vouchers may be used broadly and

27

charter laws are unrestrictive enough so that charter schools are generally available.

Here, schools that lose students are not automatically allocated other students to make up

for the loss. Newly opened or expanded private schools and charter schools can enroll

students that do not get into the “best” schools. Funding for bad schools, and the school

administrator’s payoff, will suffer for schools with continually declining enrollment.

While this creates potential for approximating open entry and exit conditions,

much depends on state laws states in this regard. The Center for Education Reform

(2013) rates states on the ease of opening, the availability, and autonomy of charter

schools. Some are quite restrictive and others are not, so there is a great deal of variation

across states as to the openness of entry via charter schools into schooling markets.

Voucher programs are still relatively unusual and, where they exist, are targeted to a

narrow group and so voucher-eligible schools cannot enter the broader schooling market.

(ii) Pricing

Related to this is the freedom of schools to set their own price (tuition). This is

severely restricted in most cases. Open enrollment and magnet programs typically carry

no price differential and charter and voucher program usually limit what schools can

charge. These cause the problems of excess demand and supply of different schools

noted above. Additionally, limits on pricing impede the ability of schools to gain by

raising V, which keeps the parameter B at a low level.

Enrollment imbalances in open enrollment programs has led some school districts

to implement school assignment protocols. These are critiqued by Pathak and Sonmez

(2013) for being unstable and manipulable. They suggest Gale-Shapley-Roth type

algorithms that lead to stable matching. However, the need for such sophisticated

28

algorithms results from limitations on pricing. Hatfield and Milgrom (2005) point out the

parallels between matching and auction models and show that, as long a price (as well as

non-price attributes) is part of the auction process, stable matching occurs. Similarly,

Chiappori, McCann, and Nesheim (2009) show that, under broad conditions, the hedonic

price equilibrium is equivalent to a stable matching equilibrium.

Thus, allowing pricing deals with these issues, as well as allowing high (low)

value provision of education to be rewarded (penalized) with a high (low) price. The fact

that most school choice reforms do not allow it serves to limit increases in B.

(iii) Politics and the Public Sector

Other parameters that distort the setting of teacher incentives – θ, δ, and φ – have

to do with the political influence on school administrators and the lack of residual

income claimancy in the public sector. With greater dependence on attracting students to

attain revenue, one expects that vouchers and charters to be less influenced by political

considerations. This implies lower values of δ and φ. Likewise, though charters and

schools that receive voucher students are mostly nonprofits, their concern about residual

income is likely to be higher than that for public schools. This serves to increase θ in

administrators’ payoff functions. Thus, charter and voucher programs that enable more

residual income claimancy and autonomy from politics are likely to be more effective

reforms.

(iv) Empirical Evaluations: Test Scores

A substantial number of empirical studies examine the effects of vouchers and

charters on student test score achievement that can shed light on whether the presumed

better governance in these settings improves schools. The literature on charter schools is

29

especially large and growing. Betts and Tang (2011) and Clark, et. al. (2011) provide

recent evidence on the effects of charters on test scores and the volume compiled by

Toma and Zimmer (2012) provides an overview of findings on charter schools. Most

studies compare large samples of charter school students to compare to regular public

school students, with various methods to control for pre-existing differences across the

two groups of students.10 Though there are statistical disputes about these methods, most

studies show positive effects on test scores for low-income students but not for others.

However, as noted above, charter schools vary widely in what they are allowed to

do regarding their ability to enter markets, their pricing, their autonomy in hiring and

admissions, their accountability, and their (non)accommodation of unions. Each of these

effects the key parameters of the school administrator’s payoff function. Variation in

these parameters generates different incentives and different expected outcomes. Studies

that fail to distinguish between these differences across charter schools are not very

meaningful. For example, tightly constrained charter schools probably will differ little

from regular public schools, so have similar incentives and similar expected outcomes.

This is not so for charters in states with unrestrictive rules.

Related comments apply to studies of voucher programs. Surveys of the

empirical literature are in Coulson (2009) and Rouse and Barrow (2009). Many studies

find positive effects of the voucher programs on student test scores, but a substantial

minority do not. However, as with some charter schools, many voucher programs in the

U.S. are quite restrictive, implying that they are likely to have only limited effects on the

10 Hoxby, et. al. (2009), however, use a narrow sample of Harlem students, with the charter students randomly selected by lottery.

30

parameters of importance: θ, B, δ, and φ. Thus, these studies probably say little about

the effect of an extensive change in school governance.

(v) Non-Cognitive Skills

Most evaluation studies, with the exception of Dobbie and Fryer (2013b), do not

consider outcomes aside from test scores. Test score outcomes matter but their extensive

use is probably due to data availability. As noted above, Heckman, Stixrud, and Urzua

(2006) show the importance of non-cognitive skills, which are not directly reflected in

test scores. Thus, if changes in school governance improve the nurturing of these non-

cognitive skills, this will not show up in the evaluation of test scores and the contribution

of charters/vouchers to educational value are understated by such studies. Dobbie and

Fryer’s (2013b) work is suggestive in this regard. They find that students in the charter

school they study in Harlem achieve higher test scores and also engage in somewhat

fewer risky behaviors, e.g., crime, pregnancy, suggesting gains beyond test scores.

A key to attaining this outcome, though, would seem to be rewarding schools for

a higher V, whether it’s from cognitive or non-cognitive skills. This entails values of θ

and B close to one.

D. Other Institutional Changes

(i) Removing Politics

Policies that isolate schools from politics move the parameters δ and φ toward one

and improve school administrator incentives. One such policy is stronger job security for

school administrators so they feel less vulnerable from politically unpopular actions.

This can reduce their sensitivity to test scores and may induce less worry about adverse

31

teacher reaction to policies. However, greater job security for school administrators

would induce less concern over value created, further reducing θ.

(ii) Parental Participation

Another possible way to tie administrator payoffs to value created is to encourage

more parental participation by various means, such as use of site-based management

councils. These councils review major school decisions and have representatives from

the school administration, teachers, and parents. The intention is that parent

representation makes the operation of the school more responsive to V, which would

increase the parameter B. However, inclusion of teachers on the council increases the

weight put on teacher utility, increasing rather than reducing φ. A further suggestion is

for school administrators to be evaluated on a basis that more closely reflects parents’

views, perhaps with use of parent satisfaction surveys.

Related to this, Duflo, Dupas, and Kremer (2012) examine a program in Kenya

that gave parents a great deal of hiring authority for their local schools. This took

decision authority out of the hands of administrators and incumbent teachers, presumably

increasing B and reducing φ. They find higher test scores for these schools, along with

reduced teacher absenteeism.

VIII. Adopting Best Practice

Recent work by Dobbie and Fryer (2013a) and Angrist, et. al. (2013) identify

particular practices of charter schools that have led to success. Fryer (2014) suggests

direct adoption of these practices into poorly performing schools. In particular, his work

on New York City charter schools identifies five school practices that separate high-

32

performing charters from low-performing ones.11 These practices were then

implemented into some of the lowest performing schools in Houston, resulting in large,

positive effects on test scores.

However, the critical question remains: what are the incentives to effectively

institute these practices? In the Houston study, school principals were specially selected

for this initiative and specific student performance goals were set for each school and the

principal was held accountable for these goals. Thus, the role of governance – in

establishing a payoff function for the school administrator to adopt effective policies and

incentivize teachers to implement them – may have been a key to the improved

performance. Study researchers apparently thought that such incentives were worthwhile

since they included them.

Additionally, an issue that arises is whether the implementation of the five

practices – in their emphasis, mix, and whether they are merged with local practices –

involves a good deal of school-specific knowledge. If it does, then it is important to

assign decision-making rights to school administrators and teachers, as well as providing

them incentives to produce value, rather than requiring a fixed regimen of protocols.

This highlights a central issue and argument of this paper. The argument is that

knowledge of “best practice” is not sufficient to yield success in school reform. Indeed,

what constitutes best practice may vary from place to place depending on local and

specific knowledge. To effectively implement these practices requires institutions with

the incentives to do so. Thus, a consideration of the parameters of the payoff function is

essential.

11 These are frequent teacher feedback, use of data to guide instruction, high-dosage tutoring, increased instructional time, and high expectations.

33

IX. Conclusion

This paper illustrates how fundamentals from principal-agent theory and the

economics of organizations are fruitfully applied to schools and teacher compensation.

Some findings are well recognized in the literature, e.g., the potential pitfalls of

mandating teacher rewards for student test scores. However, we emphasize the

importance of four institutional incentives in affecting schools and school reform: (i)

residual income claimancy and/or concentration of interests of stakeholders; (ii) the link

of school revenue/budget to value produced; (iii) the importance of public/political

symbols, and; (iv) the political strength of employees/unions. We argue that the key to

any school reform program is altering these parameters.

We assess many reform efforts regarding how the above parameters are likely to

be changed. Many seem to be lacking. Tiebout competition, though there is some

evidence of its effectiveness, is often a cumbersome method of competition and of tying

school budgets to value created. Most open enrollment programs always guarantee all

schools full enrollment (and budget), so fails to link budget to school performance.

Charter schools and voucher have the potential of emulating the entry and exit conditions

of competitive markets and are likely to have fewer political concerns than public

schools. However, many are tightly controlled, are limited in availability, and their

prices (tuition) are controlled. Each of these takes away from the potential incentives of

this reform. It is likely for this reason that studies of charter schools and vouchers find

mixed evidence of their performance. Finally, our approach suggests that injecting “best

practice” into low performing schools is likely to fail without a change in institutional

incentives, but with a favorable change in the latter, best practices will result.

34

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